More Stupid Pet Tricks

Yesterday I left my exposition of Mannian CPS just before trying to do a NH composite. There was another stupid pet trick left, that made replication of this step a little trickier than one would think.

UC had sent me a file entitled NHmean.txt (which I’ve placed online), which was produced during gridboxcps.m, and proved to be 9 unspliced of the NH reconstruction using iHAD as a “target”.

In this case, I was able to locate information at Mann’s website that could be reconciled exactly to this output (after performing a little trick.) The third column in the dataset at http://www.meteo.psu.edu/~mann/supplements/MultiproxyMeans07/data/reconstructions/cps/NH_had.csv (the column entited “cps.iHAD.”) started in AD1500 and was a splice of three columns of our NHmean.text – the first 100 years was from the AD1500 step, the next 100 years from the AD1600 step and the remainder from the AD1700 step.

The AD1800 step was left out. How? It doesn’t seem possible from the source code. But who knows? It is what it is. Another stupid pet trick.

The second reconstruction in this spreadsheet (headed “cps.HAD”) has a correlation of exactly 1 to the cps.iHAD reconstruction. It starts from the same composite (which I’ll discuss below) and is rescaled a little differently – to match the HAD instrumental series (instead of the iHAD series). It’s 1850-995 standard deviation and mean are a little different, but otherwise the series is identical. One version supposedly reconstructs land temperatures, while the other reconstructs land+ocean temperatures: the size of the glove changes depending on the person wearing it.

The column headed “cps.CRU” starts in AD200 and, unlike the other three series, had a high ( more than 0.9 correlation to the other series) but differed for inexplicable reasons – something that shouldn’t happen given the source code.

Inconsistent programming

Another weird and stupid pet trick lay here. The post-AD1700 portion had an exact correlation of 1 to the other versions – so the first leg in the splice was the AD1700 portion. For an inexplicable reason, Mann skipped the next two steps in this version – the AD1400-AD1700 portion had an exact correlation to the reconstruction step beginnning in AD1400 – so the AD1400 network was used for 300 years.

At this time, I only have Matlab output going back to AD1000 and the next steps did not have an exact correlation to any of the steps starting in AD1000 or later. The highest correlation was to the AD1000 step – it looks like this recon uses a pre-AD1000 step (perhaps AD800?) for the period up to AD1400. But only in the reconstruction with “CRU” target.

Weird. It’s hard to figure out how this would happen given the source code. I wonder if the climate models work like this.

I made a weighted average of the 15 gridcell series for the AD1000 network discussed yeaterday, weighting them by the cos latitude of the gridcell. This weighted average had a correlation of 0.9999968 to the column in the Matlab dataset NHmean that started in AD1000. So the composite matched perfectly up to scaling. Re-scaling to match the mean and sd of Mannian smoothed iHAD, the two matched up to a slight rounding discrepancy of about 0.006, as shown below. So we’ve pretty much manage to replicate all the little pet tricks so far.

Next we’ll try to figure out why some reconstructions start in AD1500 and some in AD600.

15 Comments

the first leg in the splice was the AD1700 portion. For an inexplicable reason, Mann skipped the next two steps in this version – the AD1400-AD1700 portion had an exact correlation to the reconstruction step beginnning in AD1400 – so the AD1400 network was used for 300 years.

The splicing appears to get even more bizarre in the other recons, which I’m piecing together right now. Arggh.

All proxies available within a given instrumental surface temperature grid box were then averaged and scaled to the same mean and decadal standard deviation as the nearest available 5° latitude by longitude instrumental surface temperature grid box series over the calibration period.

..and then..

The gridded proxy data were then areally weighted, spatially averaged over the target hemisphere, and scaled to have the same mean and decadal standard deviation (we refer to the latter as ‘‘variance matching’) as the target hemispheric (NH or SH) mean temperature series.

Re: UC (#5), By the way, if you calibrate a local series to temperature and then do your gridding and averaging, you should be done. You should not rescale it again against the hemispheric average–this is just an attempt to get the “right” answer. If you do the local scaling and then average all the boxes, a failure to match hemispheric data shows that something is wrong with your scheme. IMO.

By the way, if you calibrate a local series to temperature and then do your gridding and averaging, you should be done. You should not rescale it again against the hemispheric average

It is quite possible that particular geographic regions could be better or worse at reflecting global temperature conditions. Thus, giving higher emphasis to proxies from the “better” regions might give improved results. I agree strongly with you that what shouldn’t be done is to reuse the proxy data to determine the weighting scheme. Instead, the weights need to be determined solely from the measured temperature records from each of the regions. For example, simple (or even inverse) regression could be a means for “calibrating” the local temperatures to global scale. This allows for what I see as a more accurate representation of the physical situation: the proxies provide information on the local conditions and the actual local conditions give further information on the global situation. Re-using the proxies in the final stage bypasses the second step by linking the proxies directly to the global record through what can only be justified by relying on some unknown, scientifically unexplained, teleconnection mechanism.

Re: RomanM (#10), If one computes the global temperature history by weighting local instrumental records with a certain procedure, that identical procedure should be used for combining the local calibrated proxy records into a global reconstruction. I hope this clarifies what I meant.

The actual temperature history is calculated using all available global temperature records, including the regions from which no proxies were used in the study. I presume that you are suggesting that if a set of weights {wk} (for example, by gridbox area) is used in determining the global average, then the unrepresented regions are removed and the remaining ones re-weighted proportionally to their original weights. However, some regions may warm faster or slower than others due to other climate factors. Could this not possibly introduce biases into the situation based solely on the fact that proxies were or were not selected from those regions?

Several alternatives come to mind:

Expand the regions represented by given proxies based on distances between locations of the proxies before calculating area weights.

Calculate a “global record” to compare to based solely on the regions which have proxies.

Calculate a relationship between measured temperatures of the proxy-represented regions and the average global temperature (of all the regions) to determine the weights. This was what I was suggesting in my earlier post.

#12. Roman, in fairness to Mann et al, they have two methods – CPS and RegEM – the latter weights being based on correlations (as was MBH98).

I don’t think that the main issues really pertain to multivariate mechanics, but to the inconsistency of “proxies”. If every time series was temperature plus some sort of low order red noise, then almost any method would extract the underlying signal. The problem arises when you don’t know that your “proxies” really are temperature plus low-order red noise.

The sort of evidence that would most impress me at this point is the determination that some class of proxy really is a “good” proxy. And then not using any of the data used to decide that it was a “good” proxy, but getting fresh samples yielding the same result. Right now, what does any of this mean if Graybill and Ababneh get radically different bristlecones; and Briffa throws out the Polar Urals extension.